The present invention relates to a lock-in amplifier for extracting a very small input signal masked by noise in a signal measuring device.
The lock-in amplifier functions as a narrow-band filter which extracts a very small signal masked by noise. FIG. 1 shows a conventional analog lock-in amplifier. In FIG. 1 an input signal S.sub.in to an input terminal 21 is applied to a phase detector 12 via a narrow-band filter 11 which comprises an AC amplifier 11a, a band-pass filter 11b and an AC amplifier 11c. On the other hand, a reference signal S.sub.r fed to a terminal 17 is provided via a phase shifter 13 to the phase detector 12. In the phase detector 12 the input signal thereto from the narrow-band filter 11 and the reference signal S.sub.r from the phase shifter 13 are mixed by a mixer 14 which forms a synchronous detector, whereby an analog product of the two signals is produced. By this operation the center frequency component of the input signal is frequency shifted to a DC component, producing a synchronous detected output. The synchronous detected output from the mixer 14 is smoothed by an RC integrator 15 to remove noise, and the smoothed output is further amplified by a DC amplifier 16, providing a detected DC output at an output terminal 18.
Now, assuming that the amount of phase shift by the phase shifter 13 is zero and letting the input signal S.sub.in to the terminal 21 and the reference signal S.sub.r to the terminal 17 be represented by S.sub.in= Acos(2.pi.f .multidot.t+.multidot.) and S.sub.r=cos(a.pi.f.sub.c .multidot.t+.phi.), respectively, the synchronous detected output E.sub.01 available from the mixer 14 can be expressed by the following equation (1): EQU E.sub.01= .vertline.Acos(2.pi.f.multidot.t+.OMEGA.).times.cos(2.pi.f.sub.c .multidot.t+.phi.).vertline..sub.LPF =A/2 cos[2.pi.(f-f.sub.c)t+.OMEGA.-.phi.] (1)
where .OMEGA. and .phi. are the phases of the input signal S.sub.in and the reference signal S.sub.r, respectively, and the suffix LPF means that the difference component between frequencies f and f.sub.c is extracted by a low-pass filter. Since the frequency f of the input signal component which is subjected to the synchronous detection is f=f.sub.c, Eq. (1) becomes as follows: EQU E.sub.01 =A/2 cos(.OMEGA.-.phi.) (2)
A DC output voltage corresponding to the DC voltage E.sub.01 is obtained at the terminal 18. Since the phase difference (.OMEGA.-.phi.) between the input signal S.sub.in and the reference signal S.sub.r is unknown, neither the amplitude A nor the phase .OMEGA. of the input signal can be known from the measured value E.sub.01 alone. Then, by shifting the phase of the reference signal S.sub.r through 90.degree. with the phase shifter 13 and synchronously detecting the input signal S.sub.in in the same manner as described above, a DC voltage E.sub.02 expressed by the following equation (3) is obtained. EQU E.sub.02 =A/2 sin(.OMEGA.-.phi.) (3)
Calculating the sum of squared values, W=E.sub.01.sup.2 +E.sub.02.sup.2, of the thus measured voltages E.sub.01 and E.sub.02, it follows that EQU W=E.sub.01.sup.2 +E.sub.02.sup.2 =A.sup.2 /4 (4)
From this amplitude A of the input signal S.sub.in can be calculated. Further, since the phase difference (.OMEGA.-.phi.) can be obtained by calculating the ratio E.sub.02 /E.sub.01 =tan(.OMEGA.-.phi.), the phase .OMEGA. could be obtained if the phase .phi. of the reference signal S.sub.r is preknown.
In this way, the lock-in amplifier is capable of detecting from the input signal S.sub.in the amplitude of a signal component which is equal in frequency to the reference signal S.sub.r of the frequency f.sub.c and bears a fixed phase relationship thereto, that is, the amplitude of a signal component which is coherent with the phase of the reference signal S.sub.r. However, the lock-in amplifier cannot extract an AC waveform of the input signal S.sub.in nor can it extract a wide-band input signal naturally. The SN ratio of the detected DC level could be improved simply by selecting the time constant of the RC integrator 15 large, but this would inevitably increase the time for measurement. Further, such an integrating type filter cannot be employed in the extraction of the AC waveform, because it would distort the waveform.
Recently there has been placed on the market a lock-in amplifier of the type that obtains the amplitude and phase information of an input signal by a single measurement through use of two phase detectors supplied with sine and cosine waves as reference signals, respectively, instead of providing 0.degree. and 90.degree. phase shifts of the reference signal S.sub.r by the phase shifter 13 and carrying out the measurement twice as described above with regard to FIG. 1; and this lock-in amplifier is entirely made up of digital circuits. But the principle of measurement adopted in this instance is exactly the same as referred to above in connection with FIG. 1. Accordingly, this lock-in amplifier still offers no solutions to the above-mentioned problems.